We study the superconducting pairing correlations in the ground state of the doped Hubbard model—in its original form without hopping beyond nearest neighbor or other perturbing parameters—in two dimensions at intermediate to strong coupling and near optimal doping. The nature of such correlations has been a central question ever since the discovery of cuprate high-temperature superconductors. Despite unprecedented effort and tremendous progress in understanding the properties of this fundamental model, a definitive answer to whether the ground state is superconducting in the parameter regime most relevant to cuprates has proved exceedingly difficult to establish. In this work, we employ two complementary, state-of-the-art, many-body computational methods—constrained-path (CP) auxiliary-field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG) methods—deploying the most recent algorithmic advances in each. Systematic and detailed comparisons between the two methods are performed. The DMRG is extremely reliable on small width cylinders, where we use it to validate the AFQMC. The AFQMC is then used to study wide systems as well as fully periodic systems, to establish that we have reached the thermodynamic limit. The ground state is found to be nonsuperconducting in the moderate to strong coupling regime in the vicinity of optimal hole doping.

Isothermal transformations are minimally dissipative but slow processes, as the system needs to remain close to thermal equilibrium along the protocol. Here, we show that smoothly modifying the system-bath interaction can significantly speed up such transformations. In particular, we construct protocols where the overall dissipation $W_{\mathrm{diss}}$ decays with the total time ${\tau }_{\mathrm{tot}}$ of the protocol as $W_{\mathrm{diss}}\propto {\tau }_{\mathrm{tot}}^{-2\alpha -1}$, where each value $\alpha >0$ can be obtained by a suitable modification of the interaction, whereas $\alpha =0$ corresponds to a standard isothermal process where the system-bath interaction remains constant. Considering heat engines based on such speed-ups, we show that the corresponding efficiency at maximum power interpolates between the Curzon-Ahlborn efficiency for $\alpha =0$ and the Carnot efficiency for $\alpha \to \infty$. Analogous enhancements are obtained for the coefficient of performance of refrigerators. We confirm our analytical results with two numerical examples where $\alpha =1/2$, namely the time-dependent Caldeira-Leggett and resonant-level models, with strong system-environment correlations taken fully into account. We highlight the possibility of implementing our proposed speed-ups with ultracold atomic impurities and mesoscopic electronic devices.

Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin-liquid phase in the Kitaev material $\alpha \text{−}{\mathrm{RuCl}}_3$. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid’s hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to “perfectly” convert electrons from the former into emergent fermions in the latter—thereby enabling variations of transport probes invented for topological superconductors and fractional quantum-Hall states. Along the way, we resolve puzzles in the literature concerning interacting Majorana fermions, and also develop an anyon-interferometry framework that incorporates nontrivial energy-partitioning effects. Our results illuminate a partial pathway toward topological quantum computation with Kitaev materials.

The recently discovered intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has been met with unusual success in hosting emergent phenomena such as the quantum anomalous Hall effect and the axion insulator states. However, the surface-bulk correspondence of the Mn-Bi-Te family, composed by the superlatticelike ${\mathrm{MnBi}}_2{\mathrm{Te}}_4/{({\mathrm{Bi}}_2{\mathrm{Te}}_3)}_n$ ($n=0,1,2,3\dots$) layered structure, remains intriguing but elusive. Here, by using scanning tunneling microscopy and angle-resolved photoemission spectroscopy techniques, we unambiguously assign the two distinct surface states of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ ($n=1$) to the quintuple-layer (QL) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ termination and the septuple-layer (SL) ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ termination, respectively. A comparison of the experimental observations with theoretical calculations reveals diverging topological behaviors, especially the hybridization effect between the QL and SL, on the two terminations. We identify a gap on the QL termination, originating from the hybridization between the topological surface states of the QL and the bands of the SL beneath, and a gapless Dirac-cone band structure on the SL termination with time-reversal symmetry. The quasiparticle interference patterns further confirm the topological nature of the surface states for both terminations, continuing far above the Fermi energy. The QL termination carries a spin-helical Dirac state with hexagonal warping, while at the SL termination, a strongly canted helical state from the surface lies between a pair of Rashba-like splitting bands from its neighboring layer. Our work elucidates an unprecedented hybridization effect between the building blocks of the topological surface states and also reveals the termination-dependent time-reversal symmetry breaking in a magnetic topological insulator.

Soft colloids are increasingly used as model systems to address fundamental issues such as crystallization and the glass and jamming transitions. Among the available classes of soft colloids, microgels are emerging as the gold standard. Since their great internal complexity makes their theoretical characterization very hard, microgels are commonly modeled, at least in the small-deformation regime, within the simple framework of linear elasticity theory. Here we show that there exist conditions where its range of validity can be greatly extended, providing strong numerical evidence that microgels adsorbed at an interface follow the two-dimensional Hertzian theory, and hence behave like 2D elastic particles, up to very large deformations, in stark contrast to what found in bulk conditions. We are also able to estimate Young’s modulus of the individual particles and, by comparing it with its counterpart in bulk conditions, we demonstrate a significant stiffening of the polymer network at the interface. Finally, by analyzing dynamical properties, we predict multiple reentrant phenomena: By a continuous increase of particle density, microgels first arrest and then refluidify due to the high penetrability of their extended coronas. We observe this anomalous behavior in a range of experimentally accessible conditions for small and loosely cross-linked microgels. The present work thus establishes microgels at interfaces as a new model system for fundamental investigations, paving the way for the experimental synthesis and research on unique high-density liquidlike states. In addition, these results can guide the development of novel assembly and patterning strategies on surfaces and the design of novel materials with desired interfacial behavior.

We theoretically study the few- and many-body dynamics of photons in chiral waveguides. In particular, we examine pulse propagation through an ensemble of $N$ two-level systems chirally coupled to a waveguide. We show that the system supports correlated multiphoton bound states, which have a well-defined photon number $n$ and propagate through the system with a group delay scaling as $1/n^2$. This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system. For sufficiently many photons and sufficiently short systems, we show that linear combinations of $n$-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency. Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition. Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons. Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters. Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.

In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded, and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial whether such a linear light cone exists. Herein, we consider generic long-range interacting systems with decaying interactions, such as $R^{-\alpha }$ with distance $R$. We prove the existence of the linear light cone for $\alpha >2D+1$ ($D$, the spatial dimension), where we obtain the Lieb-Robinson bound as $\parallel [O_i(t),O_j]\parallel \lesssim t^{2D+1}(R-\overline{v}t{)}^{-\alpha }$ with $\overline{v}=\mathcal{O}(1)$ for two arbitrary operators $O_i$ and $O_j$ separated by a distance $R$. Moreover, we provide an explicit quantum-state transfer protocol that achieves the above bound up to a constant coefficient and violates the linear light cone for $\alpha <2D+1$. In the regime of $\alpha >2D+1$, our result characterizes the best general constraints on the information spreading.

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state $|\psi ⟩$, ${\mathcal{O}}_x(t){\mathcal{O}}_y|\psi ⟩\approx {\mathcal{O}}_y{\mathcal{O}}_x(t)|\psi ⟩$ with arbitrarily small errors—so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance $r$ interact with potential energy $V(r)\propto 1/r^{\alpha }$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state $|\psi ⟩$ when $\alpha >3$ (Lieb-Robinson light cone); for a typical state $|\psi ⟩$ chosen uniformly at random from the Hilbert space when $\alpha >\frac{5}{2}$ (Frobenius light cone); and for every state of a noninteracting system when $\alpha >2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

We introduce a new boundary condition which renders the flux-insertion argument for the Lieb-Schultz-Mattis-type theorems in two or higher dimensions free from the specific choice of system sizes. It also enables a formulation of the Lieb-Schultz-Mattis-type theorems in arbitrary dimensions in terms of the anomaly in field theories in $1+1$ dimensions with a bulk correspondence as a BF theory in $2+1$ dimensions. Furthermore, we apply the anomaly-based formulation to the constraints on a half-filled spinless fermion on a square lattice with $\pi$ flux, utilizing a time-reversal, magnetic translations and an on-site internal $\mathrm{U}(N)$ symmetries. This demonstrates the role of the time-reversal anomaly on the ingappabilities of a lattice model. Moreover, by our new boundary condition, we show that the many-body Chern number of this lattice model is nonvanishing as $N$ mod $2N$ in the presence of $\mathrm{U}(N)$ and magnetic translations. This can be a general mechanism of anomaly-based constraints on quantized Hall conductance, which generally depends on high-energy physics, from field theory.

Electron optics in the solid state promises new functionality in electronics through the possibility of realizing nano- and micrometer-sized interferometers, lenses, collimators, and beam splitters that manipulate electrons instead of light. Until now, however, such functionality has been demonstrated exclusively in one-dimensional devices, such as in nanotubes, and in graphene-based devices operating with $p\text{−}n$ junctions. In this work, we describe a novel mechanism for realizing electron optics in two dimensions. By studying a two-dimensional Fabry-Perot interferometer based on a resonant cavity formed in an InAs/GaSb double quantum well using $p\text{−}n$ junctions, we establish that electron-hole hybridization in band-inverted systems can facilitate coherent interference. With this discovery, we expand the field of electron optics in two dimensions to encompass materials that exhibit band inversion and hybridization.

Heisenberg exchange coupling between neighboring electron spins in semiconductor quantum dots provides a powerful tool for quantum information processing and simulation. Although so far unrealized, extended Heisenberg spin chains can enable long-distance quantum information transfer and the generation of nonequilibrium quantum states. In this work, we implement simultaneous, coherent exchange coupling between all nearest-neighbor pairs of spins in a quadruple quantum dot. The main challenge in implementing simultaneous exchange couplings is the nonlinear and nonlocal dependence of the exchange couplings on gate voltages. Through a combination of electrostatic simulation and theoretical modeling, we show that this challenge arises primarily due to lateral shifts of the quantum dots during gate pulses. Building on this insight, we develop two models that can be used to predict the confinement gate voltages for a desired set of exchange couplings. Although the model parameters depend on the number of exchange couplings desired (suggesting that effects in addition to lateral wave-function shifts are important), the models are sufficient to enable simultaneous and independent control of all three exchange couplings in a quadruple quantum dot. We demonstrate two-, three-, and four-spin exchange oscillations, and our data agree with simulations.

We develop a general stochastic thermodynamics of RLC electrical networks built on top of a graph-theoretical representation of the dynamics commonly used by engineers. The network is (i) open, as it contains resistors and current and voltage sources, (ii) nonisothermal, as resistors may be at different temperatures, and (iii) driven, as circuit elements may be subjected to external parametric driving. The proper description of the heat dissipated in each resistor requires care within the white-noise idealization as it depends on the network topology. Our theory provides the basis to design circuits-based thermal machines, as we illustrate by designing a refrigerator using a simple driven circuit. We also derive exact results for the low-temperature regime in which the quantum nature of the electrical noise must be taken into account. We do so using a semiclassical approach, which can be shown to coincide with a fully quantum treatment of linear circuits for which canonical quantization is possible. We use this approach to generalize the Landauer-Büttiker formula for energy currents to arbitrary time-dependent driving protocols.

We study terahertz (THz) radiation transmission through grating-gate graphene-based nanostructures. We report on room-temperature THz radiation amplification stimulated by current-driven plasmon excitation. Specifically, with an increase of the dc current under periodic charge density modulation, we observe a strong redshift of the resonant THz plasmon absorption, followed by a window of complete transparency to incoming radiation and subsequent amplification and blueshift of the resonant plasmon frequency. Our results are, to the best of our knowledge, the first experimental observation of energy transfer from dc current to plasmons leading to THz amplification. Additionally, we present a simple model offering a phenomenological description of the observed THz amplification. This model shows that in the presence of a dc current the radiation-induced correction to dissipation is sensitive to the phase shift between oscillations of carrier density and drift velocity. And, with an increasing current, the dissipation becomes negative, leading to amplification. The experimental results of this work, as all obtained at room-temperature, pave the way toward the new 2D plasmon-based, voltage-tunable THz radiation amplifiers.

Quantum metrology is a powerful tool for explorations of fundamental physical phenomena and applications in material science and biochemical analysis. While in principle the sensitivity can be improved by increasing the density of sensing particles, in practice this improvement is severely hindered by interactions between them. Here, using a dense ensemble of interacting electronic spins in diamond, we demonstrate a novel approach to quantum metrology to surpass such limitations. It is based on a new method of robust quantum control, which allows us to simultaneously suppress the undesired effects associated with spin-spin interactions, disorder, and control imperfections, enabling a fivefold enhancement in coherence time compared to state-of-the-art control sequences. Combined with optimal spin state initialization and readout directions, this allows us to achieve an ac magnetic field sensitivity well beyond the previous limit imposed by interactions, opening a new regime of high-sensitivity solid-state ensemble magnetometers.

We introduce a new approach for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are robust against disorder, unwanted interactions, and pulse imperfections. It utilizes a matrix representation of the Hamiltonian engineering protocol based on time-domain transformations of the Pauli spin operator along the quantization axis. This representation allows us to derive a concise set of algebraic conditions on the sequence matrix to engineer robust target Hamiltonians, enabling the simple yet systematic design of pulse sequences. We show that this approach provides an efficient framework to (i) treat any secular many-body Hamiltonian and engineer it into a desired form, (ii) target dominant disorder and interaction characteristics of a given system, (iii) achieve robustness against imperfections, (iv) provide optimal sequence length within given constraints, and (v) substantially accelerate numerical searches of pulse sequences. Using this systematic approach, we develop novel sets of pulse sequences for the protection of quantum coherence, optimal quantum sensing, and quantum simulation. Finally, we experimentally demonstrate the robust operation of these sequences in a system with the most general interaction form.

Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an elementary band representation (atomic limit band) splits into a particular set of bands. For the first time, we obtain a complete classification of the fragile topological phases, which can be diagnosed by symmetry eigenvalues, to find an incredibly rich structure that far surpasses that of stable or strong topological states. We find and enumerate hundreds of thousands of different fragile topological phases diagnosed by symmetry eigenvalues, and we link the mathematical structure of these phases to that of affine monoids in mathematics. Furthermore, for the first time, we predict and calculate (hundreds of realistic) materials where fragile topological bands appear, and we showcase the very best ones.

We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree cluster protects the information from transmission loss and enables long-range quantum communication through a chain of repeater stations. As opposed to conventional approaches that are limited by the two-way communication time, the overall transmission rate of the current quantum repeater protocol is determined by the local processing time enabling very high communication rates. We further show that such a repeater can be constructed with as little as two stationary qubits and one quantum emitter per repeater station, which significantly increases the experimental feasibility. We discuss potential implementations with diamond defect centers and semiconductor quantum dots efficiently coupled to photonic nanostructures and outline how such systems may be integrated into repeater stations.

High-spin states play a key role in chemical reactions found in nature. In artificial molecular systems, singlet fission produces a correlated triplet-pair state, a spin-bearing excited state that can be harnessed for more efficient solar-energy conversion and photocatalysis. In particular, triplet-pair states with overall quintet character (total spin $S=2$) have been discovered, but many of the fundamental properties of these biexciton states remain unexplored. The net spin of these pair states makes spin-sensitive probes attractive for their characterization. Combined with their surprisingly long spin coherence (of order microseconds), this opens up techniques relying on coherent spin control. Here we apply coherent manipulation of triplet-pair states to (i) isolate their spectral signatures from coexisting free triplets and (ii) selectively couple quintet and triplet states to specific nuclear spins. Using this approach, we separate quintet and triplet transitions and extract the relaxation dynamics and hyperfine couplings of the fission-borne spin states. Our results highlight the distinct properties of correlated and free triplet excitons and demonstrate optically induced nuclear spin polarization by singlet fission.

Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modeling transportation networks, social circles, and the human brain. A fundamental and still open problem is to assess if and when the multilayer representation of a system provides a qualitatively better model than the classical single-layer aggregated network. Here we tackle this problem from an algorithmic information theory perspective. We propose an intuitive way to encode a multilayer network into a bit string, and we define the complexity of a multilayer network as the ratio of the Kolmogorov complexity of the bit strings associated to the multilayer and to the corresponding aggregated graph. We find that there exists a maximum amount of additional information that a multilayer model can encode with respect to the equivalent single-layer graph. We show how our complexity measure can be used to obtain low-dimensional representations of multidimensional systems, to cluster multilayer networks into a small set of meaningful superfamilies, and to detect tipping points in the evolution of different time-varying multilayer graphs. Interestingly, the low-dimensional multiplex networks obtained with the proposed method also retain most of the dynamical properties of the original systems, as demonstrated for instance by the preservation of the epidemic threshold in the multiplex susceptible-infected-susceptible model. These results suggest that information-theoretic approaches can be effectively employed for a more systematic analysis of static and time-varying multidimensional complex systems.